Finite Group Databasebeta

← #24985867

Subgroups — #24985867

Order 11008.

418 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19141525C211yesmaximal, characteristic
2#19136159C212yesmaximal, complemented
3#19136128C211yesmaximal, characteristic
4#19132417C212yesmaximal, complemented
5C43×#1270C211yesmaximal, characteristic
6C2×#13063306—21no—
7C2×#13063256—21no—
8C2×#13063246—21no—
9#14582829—21no—
10#14582824—22no—
11#14582797C2212yes—
12#14582774—22no—
13#14582769C2211yescharacteristic
14#14582662—22no—
15#14582662—22no—
16#14582654C2211yescharacteristic
17C43×#390C2211yescharacteristic
18C43×#336C2212yes—
19C23×Dic43—21no—
20C22×C43⋊C8—21no—
21#13063306—42no—
22#13063306—42no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—22no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43D412yes—
27C2×C4⋊Dic43D412yes—
28C2×Dic43⋊C4—22no—
29C2×C22⋊Dic43—21no—
30C2×C22⋊Dic43—22no—
31#13063256—42no—
32#13063246—42no—
33C43⋊#95—21no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C22×D4×C43D411yescharacteristic
37C22×C8×C43—22no—
38C2×C4⋊C4×C43D411yescharacteristic
39C2×C22⋊C4×C43—22no—
40C2×C42×C43C2311yescharacteristic
41C24×C43—21no—
42C2×D4×C43—21no—
43C2×D4×C43—41no—
44C2×D4×C43—41no—
45C2×D4×C43SD1612yes—
46C22×C4×C43—21no—
47C22×C4×C43C2×D411yescharacteristic
48C22×C4×C43C2×D412yes—
49C22×Dic43—22no—
50C22×Dic43—22no—
51C22×Dic43—42no—
52C22×Dic43—41no—
53C22×Dic43—81no—
54C22×Dic43—81no—
55C2×C8×C43—42no—
56C2×C8×C43—42no—
57C2×C8×C43—42no—
58C4⋊C4×C43—41no—
59C22⋊C4×C43—42no—
60C22⋊C4×C43—42no—
61C42×C43—41no—
62C22⋊Dic43—42no—
63C22⋊Dic43—44no—
64C4⋊Dic43—22no—
65C4⋊Dic43—22no—
66C4⋊Dic43—42no—
67C4⋊Dic43—41no—
68C4⋊Dic43—41no—
69C4⋊Dic43—44no—
70C4⋊Dic43—81no—
71Dic43⋊C4—42no—
72Dic43⋊C4—42no—
73C2×C43⋊C8—22no—
74C2×C43⋊C8—41no—
75C2×C43⋊C8—41no—
76C23×C43—22no—
77C23×C43—42no—
78C23×C43—41no—
79C23×C43—42no—
80C23×C43—41no—
81C23×C43#12011yescharacteristic
82D4×C43—42no—
83D4×C43—81no—
84C2×C4×C43—21no—
85C2×C4×C43—22no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—42no—
89C2×C4×C43—41no—
90C2×C4×C43C2×SD1611yescharacteristic
91C2×C4×C43#13512yes—
92C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
93C2×C4×C43#13712yes—
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—42no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—42no—
100C2×Dic43—84no—
101C2×Dic43—81no—
102C2×Dic43—82no—
103C8×C43—82no—
104C43⋊C8—42no—
105#7824—431nomaximal, Sylow
106C22×C43—42no—
107C22×C43—44no—
108C22×C43—82no—
109C22×C43—81no—
110C22×C43—81no—
111C22×C43#45011yescharacteristic
112C22×C43#45212yes—
113C22×C43#45311yescharacteristic
114C22×C43#45412yes—
115C22×C43#45811yescharacteristic
116C4×C43—21no—
117C4×C43—21no—
118C4×C43—22no—
119C4×C43—22no—
120C4×C43—81no—
121Dic43—82no—
122Dic43—82no—
123Dic43—161no—
124#2724—431no—
125#2100—432no—
126#2094—431no—
127#1271—432no—
128#1270D4311yescharacteristic
129C2×C43—82no—
130C2×C43#161311yescharacteristic
131C2×C43#161512yes—
132C2×C43#163011yescharacteristic
133C2×C43#163512yes—
134C2×C43#165711yescharacteristic
135C2×#123—861no—
136C2×#106—861no—
137C2×#102—861no—
138#398—861no—
139#397—862no—
140#390C2×D4311yescharacteristic
141#389—432no—
142#385—862no—
143#384—431no—
144#340—862no—
145#340—862no—
146#336—431no—
147#336C2×D4312yes—
148C43#782411yescharacteristic, complemented, Sylow
149C22×D4D17211yescharacteristic
150C23×C4—861no—
151C22×C8—22no—
152C22×C8—861no—
153#123—1722no—
154#123—1722no—
155C2×C4⋊C4—432no—
156C2×C4⋊C4—432no—
157C2×C4⋊C4—861no—
158C2×C4⋊C4—862no—
159C2×C4⋊C4—861no—
160C2×C4⋊C4—862no—
161C2×C4⋊C4D17211yescharacteristic
162C2×C22⋊C4—22no—
163C2×C22⋊C4—862no—
164C2×C22⋊C4—861no—
165C2×C42C22×D4311yescharacteristic
166#106—1722no—
167#102—1722no—
168#95—862no—
169#95—861no—
170#95—862no—
171C24—21no—
172C2×D4—21no—
173C2×D4—41no—
174C2×D4—41no—
175C2×D4#1062187312yes—
176C22×C4—21no—
177C22×C4—862no—
178C22×C4—862no—
179C22×C4—3441no—
180C22×C4—3441no—
181C22×C4—1721no—
182C22×C4—1722no—
183C22×C4C2×D17211yescharacteristic
184C22×C4D4×D4312yes—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—862no—
189C2×C8—1721no—
190C2×C8—1721no—
191C4⋊C4—41no—
192C4⋊C4—862no—
193C4⋊C4—862no—
194C4⋊C4—3441no—
195C4⋊C4—1721no—
196C4⋊C4—1721no—
197C4⋊C4—1724no—
198C4⋊C4—1722no—
199C4⋊C4—1722no—
200C4⋊C4—1722no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C22⋊C4—1722no—
204C22⋊C4—1724no—
205C42—41no—
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23#1306329511yescharacteristic
212D4—42no—
213D4—81no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—3444no—
221C2×C4—3441no—
222C2×C4—3442no—
223C2×C4—1722no—
224C2×C4—1722no—
225C2×C4—1722no—
226C2×C4—1722no—
227C2×C4—1722no—
228C2×C4—1722no—
229C2×C4C2×#1062187311yescharacteristic
230C2×C4#1306334412yes—
231C2×C4#1306335311yescharacteristic
232C2×C4#1306335412yes—
233C8—82no—
234C8—1722no—
235C22—44no—
236C22—42no—
237C22—81no—
238C22—82no—
239C22—81no—
240C22#1458305211yescharacteristic
241C22#1458306212yes—
242C22#1458306911yescharacteristic
243C22#1458307312yes—
244C22#1458309011yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—81no—
250C4—3442no—
251C4—3442no—
252C4—6881no—
253C2—82no—
254C2#1913361711yescharacteristic
255C2#1913362712yes—
256C2#1913371711yescharacteristic
257C2#1913374812yes—
258C2#1913389411yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1270C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenter#1270D43
hypocenterC43#7824
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19136159C2semidirect
4. #19132417C2semidirect
148. C43#7824semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191415252
#191361592
#191361282
#191324172
C43×#12702
#782443